Linear Algebra Exercise — Topic 2 of Machine Learning Foundations

In this video from my Machine Learning Foundations series, I provide an applied linear algebra exercise (involving solar panels) to challenge your understanding of the content from the preceding video.

[Hsnfci]

So to follow
Amount(Mark 1) =(T+30)* 1 ( Where T unit day)
Amount(Mark 2) = T*4

So when both two amounts are equal
(T+30) *1 = T*4
T+30 = 4T
30 = 4T-T
30 = 3T
T=10

so after 10 days both amount should be equal which is on May 10th
and the total amount will be generated is
(10+30) + 4*10 = 80 kj

and of course if they are generating both amounts per day there will be no intersection.


Cheers Dr. Jon

[Ossigen]

hello, i'm 16 years old from italy, i've tried a lot of course on youtube for machine learning but they just didn't mean nothing to me, i was just using function of a library, then i cath this course and finally things is starting to get more sense, thank you.

ps: i'm at the third year in highschool and we just arrived at the matrix in math, but i hope i can understand everything even if i'm not that good at math in school !

[gauravsonawane]

Here is the way how I framed this problem:

mark 1 make - 1kj => e1 = 1kj * days
mark 2 makes - 4kj => e2 = 4kj * days

find out when they would make equally same energy

e1 = e2 (I don't know if here, I can say, LHS = RHS )

1kj*days = 4kj*days <---- lets add twist here, it is 30 days late
1kj*days = 4kj*(days-30days) // I wrote it like this to make it clear to understand, so

actual problem: 1kj (d) = 4kj (d-30) ----> solve it

answer would be 40 days, to become equal, means to make equal energy
and to find the total energy, yaa it's so easy >>---> replace days with 40 in above eq, [ no that 30 days ]

And now you can solve I know. 😁

[finncollins]

hey Jon, got the answer. thanks once again for this tutorial series....

[hcdebey]

It seems that there is a slight mixup of terms. At 2:04, It is stated that power is produced at 1 kJ/day. I believe that a kJ is a unit of energy, not power.

[jamescarpenter]

Jon, I'm having trouble understanding when I would use parenthesis while using linear algebra to solve real world problems such as this. For example in this equation I can understand that -30 represents the days of the month that the Mark ll has effectively missed/skipped, and I can understand the 1KJ of power for the Mark l and the 4KJ of power for the Mark ll. With this, I initially thought the way to solve this problem was 1KJ = 4KJ - 30 rather than 1KJ = 4(KJ - 30). My question is, when I'm trying to think about a simple equation like this logically, how would I think to use parenthesis? In other words, how would you explain to me in very plain and simple English the parenthesis in this equation?

EDIT - Ok this was super confusing for me but I think I figured it out... Could it also be 1(d+30) = 4d ? I had the parenthesis on the other side to start, but it just didn't make sense in my mind. Having it this way makes the think "the Mark l started a month early, so we are giving it an EXTRA 30 days rather than SUBTRACTING 30 days of power from the Mark l"... Are there any advantages or disadvantages by doing it this way? Jeez I just spent half an hour thinking about this... was bothering my brain...

[munimshah]

I went...

(1*30)+t=4t

30+t= 4t
---- ----
-t -t
30 = 3t
----
3 3

10=t

10 + 30 = 40 days aka May 10th

Did it in my head like this. Didn't think it would be right, but it was. If anyone can explain why I would appreciate it!

[travail]

Mmm this needs a little explanation, no? Not just giving the solutons, at least gives us the x, y axis you used and where does the data fit in the y=ax+b

[puneetsethi]

hey Jon, I got the answer to be:
1* t = 4* (t-31)
1T = 4t - 124
T-4t = -124
-3t = -124
=> 41.33
what did i missed?

[yxcqwertzubn]

why you put that thing in front of your door

[surfingcipher]

tried my hand at the plot of it

import numpy as np
import matplotlib.pyplot as plt
t = np.linspace(0, 50, 1000) # start, finish, n points

M_1 = (t+30)*1
M_2 = t * 4

fig, ax = plt.subplots()
plt.title('Solar panel')
plt.xlabel('time (in days)')
plt.ylabel('Energy (in joules)')
ax.set_xlim([0, 30])
ax.set_ylim([0, 50])
ax.plot(t, M_1, c='green')
ax.plot(t, M_2, c='brown')
plt.axvline(x=10, color='purple', linestyle='--')
_ = plt.axhline(y=40, color='purple', linestyle='--')
plt.show()
my brother john, very impressive series.